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Elenna [48]
4 years ago
12

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel st

raight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the actual track (the shaded region).

Mathematics
1 answer:
Nostrana [21]4 years ago
3 0
First we calculate the area of each semicircle (half the area of the full circle)
and we substract them to get the area of the curved shaded part

1/2 * [ pi * (80/2)**2 ] - 1/2 * [ pi * (60/2)**2 ] = (800-450)pi = 350*pi m2

the area of the full circle   (both sides) ------------2*350*pi m2--750*pi m2

The area of the straight line = 2 * (100 *10) = 2000 m2

Total Area = 2000 +700*pi m2 = 4198 m2
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B. 5\times10^{2}

Step-by-step explanation:

We are told that the smallest object visible with our eyes is similar to the width of a piece of hair, which is 1\times 10^{-4} meters wide.

Using an optical microscope, we can see items up to 2\times 10^{-7} meters wide.

To find the objects we can see with our eyes are how much larger than the objects we can see with an optical microscope, we can set an equation as:

\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=\frac{1*10^{-4}}{2*10^{-7}}

Using the exponent rule of quotient \frac{a^m}{a^n}=a^{m-n} we will get,

\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=\frac{1}{2}*10^{-4-(-7)}

\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^{-4+7}

\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^{3}

\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10\times 10^{3-1}

\text{The object we can see with our eyes}=5\times10^{2}*\text{The objects we can see with microscope}

Therefore, the objects we can see with our eyes are 5\times10^{2} times larger than the objects we can see with an optical microscope and option B is the correct choice.

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3 years ago
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